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3 years ago

What is the length of AC¯¯¯¯¯

Mathematics

2 answers:

Nutka1998 [239]3 years ago

5 0

Answer: AC=12 cm

Step-by-step explanation:

To solve this problem you must apply the law of sines, as you can see below:

$\frac{a}{sinA}=\frac{b}{sinB}$

Where:

a=13

A=85.2°

B=71.6°

Therefore, you must solve for b, then, you obtain that the lenght AC asked in the problem above is:

$b={sinB}*\frac{a}{sinA}\\b=\frac{sin(71.6)*13}{sin(85.2)}\\b=12$

Serggg [28]3 years ago

5 0

ANSWER
$AC=12cm$

EXPLANATION

We use the sine rule to obtain,

$\frac{AC}{ \sin(71.6 \degree) } = \frac{13}{ \sin(85.2 \degree) }$

We solve for AC to obtain,

$AC= \frac{13}{ \sin(85.2 \degree) } \times \sin(71.6 \degree)$

We simplify and round to the nearest whole number to obtain,

$AC= 12cm$

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3 years ago

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Aleonysh [2.5K]

Answer:

A. $y=3x-10$

C. $y+6=3(x-15)$

Step-by-step explanation:

Given:

The given line is $6x+18y=5$

Express this in slope-intercept form $y=mx+b$ , where m is the slope and b is the y-intercept.

$6x+18y=5\\18y=-6x+5\\y=-\frac{6}{18}x+\frac{5}{18}\\y=-\frac{1}{3}x+\frac{5}{18}$

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Let us find the slopes of each lines.

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On comparing with the slope-intercept form, we get slope as $m_{A}=3$ .

Now, $m\times m_{A}=-\frac{1}{3}\times 3=-1$ . So, option A is perpendicular to the given line.

Option B:

For lines of the form $x=a$ , where, a is a constant, the slope is undefined. So, option B is incorrect.

Option C:

On comparing with the slope-point form, we get slope as $m_{C}=3$ .

Now, $m\times m_{C}=-\frac{1}{3}\times 3=-1$ . So, option C is perpendicular to the given line.

Option D:

$3x+9y=8\\9y=-3x+8\\y=-\frac{3}{9}x+\frac{8}{9}\\y=-\frac{1}{3}x+\frac{8}{9}$

On comparing with the slope-intercept form, we get slope as $m_{D}=-\frac{1}{3}$ .

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3 years ago

Write an equation of the line in slope-intercept form. JY 1 (3, 3) (0, 2) 2 4 y=

stellarik [79]

Correct answer: y = $\frac{1}{3}$ x + 2

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m = $\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$ → $\frac{2-3}{0-3}$ → $\frac{-1}{-3}$ → $\frac{1}{3}$

To find out the y-intercept, just substitute (3, 3) into the slope-intercept formula ( y = mx + b ) with the slope that is substituted for 'm' that we already solved earlier.

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3 = 1 + b

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You can also prove this true by looking at the graph provided. The line intersects at the y-axis at 2.

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